Distributed mobility and power control for noncooperative robotic ad hoc and sensor networks

In this paper we propose novel algorithms for noncooperative power and position control in mobile ad hoc networks. The algorithms are distributed and adaptive, i.e., they are able to deal with the agents´ lack of knowledge about the environmental conditions and about the actions, positions and properties of the other agents, which is the essential challenge in these networks. The agents´ cost functions consist of a term proportional to the achievable rate of communication with the neighbors, explicitly depending on the interference from the other agents, and a pricing term penalizing excessive power (for the power control scheme) or deviation from predefined positions (for the position control scheme). We formulate conditions for the existence and uniqueness of the Nash equilibrium and prove that the algorithms converge to it almost surely, based only on local measurements and local signaling between the neighbors. The position control algorithm can be adopted to specific motion dynamics of the networked mobile robots. We illustrate the main properties of the algorithms through simulations.